where \(\log p(\vec{d}(t)|\vec{n})\)  is the natural logarithm of the noise likelihood defined as [1]}
\(\log p(\vec{d}(t)|\vec{n}) = - \frac{1}{2} \sum _{i=1}^{N} \left< \tilde{d}_{i}(f) | \tilde{d}_{i}(f) \right> \,.\) 
